Direction and distance correcting golf putter

ABSTRACT

A golf putter has a putter head with an actively compliant beam which is parallel to the face of the putter. The beam connects to a shaft along its length and is separated from the head except for its ends. The force of impact between the face of the putter and the ball on the putter face sweet spot causes a stress to develop in the beam, resulting in a deflection in the beam proportional to the force of the impact, while maintaining the putter face orientation with respect to the putting line. Impacts which miss the sweet spot will cause the putter face to skew to an angle with respect to the putting line, also introducing a proportional flexure of the beam, depending on the distance between the sweet spot and the point of impact. The beam has a characteristic time such that as the force between the ball and the putter face decreases to zero after impact, the beam flexure simultaneously recovers causing the putter face to return to its original putting line orientation at almost the same instant the ball leaves the putter face, thereby providing distance and directional correction for mishit putts. Additionally, when a putter head with a suitable moment of inertia is coupled with an actively compliant beam, feel and alignment are substantially enhanced. The putter also uses a unique visual alignment sight line groove on the top surface of the putter head, extending from the face to the back of the putter. The groove is perpendicular to the face of the putter and may have tapered side walls. It is positioned directly above and parallel to the center of mass and the sweet spot, so that it can be positioned directly over the intended putting line when the putter is properly located on the putting surface. The base of the groove has contrasting stripes, so that when the golfer&#39;s dominant eye is properly located over the groove, the entire stripped base of the groove is visible to the golfer.

BACKGROUND OF THE INVENTION

It is generally accepted that preparation for a putt begins with theability of the golfer to read the character of the green (with regard toslope, speed, grain direction, ball break, etc.) so that a properputting line can be selected. While somewhat intuitive for a fewgolfers, this ability is usually developed as a result of practicalexperience which enables a golfer to develop a useful technique. Evenso, it is normal even for many professional golfers to call on theservices of their caddy for help in selecting a putting line and asuggestion of required ball speed. This step is so important, manygolfers make use of a largely discredited technique called plumbbobbing, i.e. using the putter's shaft as a vertical reference guide.Still, a patent designed in accordance with U.S. Pat. No. 6,358,162 hasbeen found to be United States Golf Association (USGA) conforming. Thisdesign provides accurate horizontal and vertical references, and hasproven useful in estimating the slope of a green in all directions,especially around the hole, as well as confirming whether the flag pole,trees, fences and fence post references are truly vertical orhorizontal.

Once a putting line has been selected, the golfer is faced with the needto impact the ball with enough putter head force for the ball to reachthe hole while rolling on the intended putting line, without rolling toofar past the hole if it does not drop. It is generally agreed that arepeatable technique is a prime and exquisitely difficult task toachieve, not only for tempo to control distance, but also to maintainputter face orientation to the intended putting line.

Every golfer has individual idiosyncrasies that can introduce variationsin the swing path, face orientation and/or timing, so that the sameresult is not achieved even on repeated attempts to hole a putt of morethan a few feet. As a result, putter designers concentrate onincorporating design elements which are either passive or active tocompensate for these idiosyncrasies. In general, on almost all putts,golfers try to impact the ball on the putter's sweet spot, with theputter face perpendicular to the intended putting line. Passive elementsinclude features which provide better ball aiming and alignment guides.In addition, incorporating a high moment of inertia passively reducesthe magnitude of skewing of the putter face when the putter does notimpact the ball on the putter's sweet spot. Active design elementsinclude features such as elastomeric face inserts on the face of theputter where the ball is impacted, the flexing of which increases thedwell time of the ball on the putter face. This is intended to providethe putter face more time to square up to the putting line on impactswhich miss the sweet spot and also to enhance feel.

All of these techniques result in various degrees of forgiveness and areregularly sought after by golfers at all levels of proficiency, sincethe saving of a single stroke can result in a score reduction of as muchas 1.5% or more by a professional golfer, and as much as 1% by thoseless skilled. Since an 18 hole round of golf at par allows 36 strokes,it is easy to see how improvement in this single aspect of the game isso important.

SUMMARY OF THE INVENTION

The design intent of the putter of the present invention is to provideboth passive and active design enhancement elements. As previouslymentioned, passive improvements reduce the magnitude of the errorsintroduced by mishit balls, while active enhancements are intended tocorrect such errors, providing a larger degree of forgiveness. Activeenhancement is accomplished by the invention by the introduction of anactively compliant beam which makes use of energy stored in the beamwhen it is stressed during ball impact and which is released in a timelyfashion, thus bringing the putter face back square to the putting lineat the instant of ball and putter face separation. Passive enhancementtakes the form of strategically placed visual alignment groove sightlines on the top surface or crown of the putter. This feature results intruer alignment with the intended putting line during set up.

More specifically, the golf putter of the present invention comprises ahead of an esthetically appropriate shape combined with an activelycompliant beam which is parallel to the face of the putter. The beamconnects to a shaft at a suitable location along its length and isseparated from the head except for its ends. The force of impact betweenthe face of the putter and the ball on the putter face sweet spot causesa stress to develop in the beam, resulting in a deflection in the beamproportional to the force of the impact, while maintaining the putterface orientation with respect to the putting line. Impacts which missthe sweet spot will cause the putter face to skew to an angle withrespect to the putting line, also introducing a proportional flexure ofthe beam, depending on the distance between the sweet spot and the pointof impact. The beam has a characteristic time such that as the forcebetween the ball and the putter face decreases to zero after impact, thebeam flexure simultaneously recovers causing the putter face to returnto its original putting line orientation at almost the same instant theball leaves the putter face, thereby providing distance and directionalcorrection for mishit putts. Additionally, when a putter head with asuitable moment of inertia is coupled with an actively compliant beam,feel via the sense of sound, touch and alignment are substantiallyenhanced.

Used in combination with this unique putter head design is a visualalignment sight line groove on the top surface of the head, extendingfrom the face to the back of the putter. The groove is perpendicular tothe face of the putter and may have tapered side walls. It is positioneddirectly above and parallel to the center of mass and the sweet spot, sothat it can be positioned directly over the intended putting line whenthe putter is properly located on the putting surface. The base of thegroove has contrasting stripes, so that when the golfer's dominant eyeis properly located over the groove, the entire stripped base of thegroove is visible to the golfer.

Novel features which are considered as characteristic of the inventionare set forth in particular in the attendant claims. The inventionitself, however, both as to its design, construction and use, togetherwith the additional features and advantages thereof, are best understoodupon review of the following detailed description with reference to theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an isometric view of the putter of the present invention.

FIG. 2 is a top view of the putter head of the present application.

FIG. 3 is a front view of the putter head of the present application.

FIG. 4 is an elevation view of the putter head of the presentapplication.

FIGS. 5 a-5 d are illustrations of commonly occurring golf ball toputter head impact and movement.

FIGS. 6 a-6 d are illustrations of golf ball to putter head impact andmovement employing the putter of the present invention.

FIG. 7 is a graphic representation of test results.

FIGS. 8 a-8 d are top views of other design embodiments of putter headsemploying the present invention.

FIGS. 9 a-9 b are front views of other design embodiments of putterheads employing the present invention.

FIG. 10 shows a connection between a beam section of the presentinvention and a perimeter wall member of the putter head.

FIGS. 11 a-11 c are cross-sectional views showing various stages of theconnection process.

FIG. 12 shows a connection between the beam sections and central beamsection of the present invention.

FIGS. 13 a-13 c are cross-sectional views showing various stages of theconnection process.

FIG. 14 is a graph showing test results of putter beams' deflectionunder load.

FIG. 15 a is a plan view of a putter illustrating a correct putter hit.

FIGS. 15 b and 15 c are plan views of putters illustrating puttermishits due to improper dominant eye location.

FIG. 16 is a plan view of the putter of the present invention employingthe sight alignment configuration of the present invention.

FIG. 17 is a section view taken from FIG. 16.

FIG. 18 is a front view, similar to FIG. 17 but in a larger scale,showing sight alignment technique.

FIG. 19 a is a plan view of a conventional putter employing the sightalignment configuration of the present invention.

FIGS. 19 b and 19 c are plan views of putters illustrating additionalputter mishits due to improper dominant eye location.

DETAILED DESCRIPTION OF THE INVENTION The Beam Putter

The preferred embodiment of the present invention, shown in FIGS. 1-4,comprises golf club 1 with golf shaft 2 and golf head 4. Head 4 can beprovided with any number of different hosel designs and connectionswell-known in the industry and accepted by the USGA. While the shaftsused on most standard putters fall in the 17-18 degree angle range, USGArequirements state that when a putter is soled to the putting surface inthe normal manner, the shaft must have a tilt angle greater than 10degrees from the vertical axis.

Head 4 of the present invention comprises unitary body 6 withtransversely extending front member 8 having ball impact surface or face10 and opposite back surface 12. As seen most clearly in FIG. 4, face 10is offset at a slight angle 5, e.g. 4 degrees, from the vertical axis.Extending from member 8 are forward perimeter wall member 14 havingforward section 16 and rear perimeter wall member 18 having rearwardsection 20. Wall members 14 and 18 extend the length of head 4, fromfront member 8 to back section member 41 which terminates at back end 22of the head. Perimeter wall members 14 and 18 substantially surround anopening through unitary body 6. The opening comprises two small openings19 a and 19 b. Head 4 has substantially flat top surface or crown 9 anda bottom surface comprising substantial planar sole 11 and minimallycurved bottom surfaces 13 and 15. Weight balance port 17 is provided forthe insertion or removal of added ballast material as needed to head 4.

Actively compliant beam 30 comprises beam section 32 connected to wallmember 14 at forward section 16 and central beam section 34, and beamsection 36 connected to wall member 18 at rearward section 20 andcentral beam section 34. Beam 30 is positioned within the opening inunitary body 6, separating the opening into the smaller openings 19 aand 19 b. Shaft channel 38, within central beam section 34, foracceptance and connection of shaft 2 at USGA prescribed requirements, isprovided. FIG. 3 shows shaft placement at approximately a 17 degreeangle from the vertical axis. Putter shaft to putter head connection canbe made by directly securing the shaft at an angle to beam 30, as shown,or inserting the shaft substantially perpendicular to the beam, afterhaving it bent to the desired angle. It is also possible to connect theshaft by use of a hosel. Thus, different shaft to head angles can beaccomplished by angling the shaft or using a separate angled hosel, bentto the angle of choice, inserted into beam 30.

While not to be considered restricted to specific size, typical exemplardimensions for head 4, for reference only to show compliance with USGArequirements, would be 4⅞″ from forward section 16 to rearward section20, 4⅝″ from face 10 to back end 22, and 0.97″ from crown 9 to sole 11.Thicknesses of beam sections 32 and 36 of compliant beam 30 are also notto be considered restricted to any particular dimension. However, beamsections which are 3/32″ in thickness have been shown to be one ofseveral optimal designs. It is contemplated that typical exemplarweights of putter heads will be between 200 and 600 grams.

Indented into crown 9 are sighting alignment grooves 40 and 42 which areintended to lie directly on the putting line and above the putter faceto the back axis, through the putter's sweet spot and above its centerof mass. Arrow 44 indented into central beam section 34 and adjacentarrow 46 point in the direction of the impact portion of stroke. Reararrowed section 45 of head 4 also provides for efficient easy adjustmentof head “face to back” balance by permitting the addition or removal ofballast weight material to weight balance port 17. The configuration ofarrowed section 41 assists in club takeaway movement so that both thetakeaway and impact portions of the putting stroke are aligned with andon the intended putting line.

In use, the putting force of impact between face 10 of putter head 4 andthe ball on the putter's sweet spot causes a stress to develop with beam30, resulting in a deflection in the beam proportional to the force ofthe impact, while maintaining the putter face's orientation with respectto the putting line. Impacts which miss the sweet spot will cause putterface 10 to skew with respect to the putting line, also introducing aproportional flexure of beam 30, depending on the distance between thesweet spot and the point of impact. Beam 30 has a “characteristic time”such that as the force between the ball and putter face 10 decreases tozero as the ball starts to leave the putter face, the beamsimultaneously recovers from flexure, causing the putter face to returnto its original putting line orientation at almost the same instant theball leaves the putting face. Distance and directional correction formishit putts is the result.

Testing has revealed that if a golf ball of average hardness is struckwith a relatively instantaneous (0.5-1.2 milliseconds) force of 24.7pounds, the ball will leave the face of the putter with an initialvelocity of 6.35 feet/second. This is the velocity of a ball at theinstant it leaves a Stimpmeter, a commonly used device designed toprovide a measure of green speed, prior to making contact with a puttingsurface.

To understand the significant advancement and benefit obtained when aputter head is provided with the actively compliant beam of the presentinvention, it is helpful to review the effect of a mishit with aconventional mallet putter. Such is represented in FIGS. 5 a-5 d. Thesefigures, as well as FIGS. 6 a-6 d, are for a righthanded golfer and omitthe shaft in order to focus attention on the ball and headrelationships. Note, however, that the shaft location is intended for ashaft passing through the center of mass of the putter head. However,the same results will be observed if the shaft intersects anywhere onthe face to back axis which is perpendicular to the face of the putterand passes through the center of mass, as is common on many puttersusing shafts or hosels with one or more bends. Visualization is formotion from right to left, the center of mass being directly above theintended putting line for a sweet spot impact. It is noted that themagnitude of the rotation and deflections are enhanced for illustrativepurposes.

FIG. 5 a illustrates ball 100 and conventional putter head 50 positionedat the instant before impact. FIG. 5 b illustrates the positions ofmishit ball 100 and head 50 slightly after impact. FIG. 5 c indicatesmaximum ball compression and is the point at which the compressionstarts to reduce as the ball velocity exceeds that of head 50. While theinitial direction of the ball travel path or putting line is indicatedat 60, it is clear that ball 100 also rolls somewhat up putter face 52towards toe 54, initiating clockwise ball rotation 56 while the ball andputter face are still in contact. This continues after ball 100 leavesthe putter face in direction 58. FIG. 5 d indicates recovery of putterface 52 perpendicular to the originally intended putting line 60, wellafter ball 100 has left the putter face traveling in undesired direction59. Since ball 100 has a clockwise rotation, contact of the ball withthe ground will cause the ball to “fade” and the direction of the balltravel 59 will be even more skewed (it is actually an arc) than thedirection of travel 58 in FIG. 5 c.

It is important to realize that the rotation of head 50 is a function ofthe torsional stresses produced in the shaft and grip as a result of theimpact torque. Because these torsional rotations occur over a relativelylarge distance, recovery time is much too long to correct faceorientation while ball 100 is still in contact with putter face 52.

FIGS. 6 a-6 d show the effect of a mishit when ball 100 is struck withthe golf putter head of the present invention. FIG. 6 a illustrates theposition of mishit ball 100 in relation to putter head 4 with beam 30 ofthe present invention at the instant prior to impact. FIG. 6 billustrates the point of maximum flexure 31 a and 31 b of beam 30, whichis consistent with maximum ball compression, similar to that which isshown in FIG. 5 c, in which ball 100 could potentially be misdirected62. However, there is a finite time period, which is identified as the“characteristic time”, during which the velocity of ball 100 and thevelocity of putter head 4 are identical. During this period, beamflexure 31 a and 31 b is recovered and putter face 10 is returnedtowards being perpendicular to intended putting line 60. FIG. 6 c showsthe instant at which putter face 10 is returned to perpendicular inrelation to putting line 60 and ball 100 leaves the putter face indirection 64, parallel to the putting line. It is evident that thedesign of beam 30 is critical in achieving this characteristic timewhich is the fundamental principle employed by the putter. In FIG. 6 d,ball 100 has left putter face 10. However, although the energy stored inbeam 30 due to the impact produces a harmonic oscillation which rotatesputter face 10 so it is no longer perpendicular to putting line 60, itis of no consequence if the characteristic time is correct.

The importance of the characteristic time can be easily visualized. Ifthe characteristic time is too short, putter face 10 will rotate pastbeing perpendicular to putting line 60 and the putter face will presenta closed relationship to ball 100. If the characteristic time is toolong, putter face 10 will not have reached the targeted perpendicularposition.

Beam Putter Development

Subsequent to the decision to pursue the beam putter head concept, inputfrom the USGA was sought to determine whether the concept could meet theconformance requirements called for in the Design Of Clubsspecification. Involvement of the USGA is integral to advancing golfequipment technology; and its guidance is extremely helpful to designersand manufacturers.

Because of its unique design, information regarding the requirements forthe putter to be plain in shape, to be rigid, and to ensure it did notincorporate a tuning fork were considered and examined. While the woodenmodels displayed satisfied the plain in shape requirement, it was agreedthat rigidity and the lack of tuning fork attributes could only besatisfied by hands on testing of models made to evaluate thesecharacteristics.

At the outset, it was agreed that the use of the word rigid was a verysubjective term since when subjected to a load, it is probable thatalmost everything will move to a greater or lesser degree. At questionwas how much movement, or deflection, of the beam would be acceptableunder manual loading. In the absence of a rigidity test specificationfor beamlike or similar elements of a putter (although one does existfor elastomeric inserts in the face of a putter as well as for theflexure in the face of woods and irons), it was agreed that the USGAwould be provided with a testing apparatus and beams designed toevaluate the thickness of various beams with fixed length and heightdimensions as they might be incorporated into actual production models.Test results for sample beams that were tested by deflection under loadby use of a beam deflection testing apparatus are shown in FIG. 14.

The testing apparatus was designed so that manual force could be appliedto the beam to determine whether movement of the beam could be discernedphysically or visually. The test apparatus and results were provided tothe USGA and it was concluded and agreed that a 0.100 inch thick beamwith the length and height dimensions as shown and provided would meetthe rigidity requirement. Note that while all these test beams were madeof 6061-T5 aluminum, equivalent beams using other materials could bedesigned. It is necessary to recognize that any prototype ormodification to a design previously found conforming is subject to USGAreview in order to ensure that any such changes or unforeseen deviationsin the manufacture of production clubs does not deviate from designspreviously found conforming.

With the beam rigidity requirement resolved, the question of whether thebeam could vibrate and produce a tunable sound like a tuning fork wasstudied. Although it is clear that the sounds generated by the impact ofthe putter head and a ball cover a wide frequency range, these soundsare a function of head design and shaft location. Accordingly, sampleputter heads were built both with and without the beam and provided tothe USGA. While the putter with the beam was suspended by the attachedshaft during the test, the beam free putter head was suspended by finethreads at its corners. When each head was struck by a ball impacting atvarious locations along the putter face, it was found that there was noidentifiable audible difference in sound frequency, confirming that thesound generated was a function of head design and not beam vibration. Asa result, it was agreed that the beam putter concept met the tuning forkrequirement.

Beam Putter Calculations

It is obvious that the number of beam designs that would be useful inthis application are virtually endless. Of primary concern is themaximum beam deflection under manual load that would meet the rigidityrequirements of the USGA. For this reason, calculations were limited toa simple flat beam fixed at each end with the load applied at the beamcenter. A useful compendium of beam formula for many other beam designs,including stresses and deflections, is found in the twenty secondedition of the Machinery Handbook (22nd Edition) published by IndustrialPress Inc., 200 Madison Ave., New York, N.Y., 10016.

The equation for the maximum deflection under load of the beam describedabove is given as Case 19 in the Machinery Handbook as:

$\begin{matrix}{{y = {\frac{{Wl}^{3}}{192{EI}}\mspace{14mu}{where}}}{{y = {deflection}},{inches}}{{W = {{load}\mspace{14mu}{on}\mspace{14mu}{the}\mspace{14mu}{beam}}},{pounds}}{{l = {{beam}\mspace{14mu}{length}}},{inches}}{{E = {{Modulus}\mspace{14mu}{of}\mspace{14mu}{Elasticity}}},\mspace{14mu}{and}}{I = {{Moment}\mspace{14mu}{of}\mspace{14mu}{Inertia}}}{and}} & (1) \\{{I = {\frac{{bd}^{3}}{12}\mspace{14mu}{where}}}{{b = {{beam}\mspace{14mu}{width}}},{{inches}\mspace{14mu}{and}}}{{d = {{beam}\mspace{14mu}{thickness}}},{inches}}} & (2)\end{matrix}$

Note that I, the Moment of Inertia for a beam, differs from I the Momentof Inertia for a mass moving around an axis, as indicated in torqueinertia equations I=Σmr² and T=Ia, where m is elemental mass, r isradius, T is torque and a is angular acceleration. In this case, theresistance to change of location of a moving mass is a function of theangular acceleration of the mass around its axis of rotation. I, theMoment of Inertia of a beam results in a change of shape of the beamunder load, and reflects the beams rigidity.

Values for E, the Modulus of Elasticity for various materials have beenreported as follows, all in millions of pounds per square inch.

Aluminum (T6061 alloy, heat treated and aged) 10.0–11.4 (depending ontemper) Brass (360 Alloy) 14–17 (depending on temper) Steel (B1112,C1213 and most other Alloys) 30 Stainless (303 and most other SS Alloys)28 Tin Bronze (cast)   10–14.5 (depending on alloy) Alum. Bronze (cast)15–18 (depending on alloy) Titanium (6AL—4V, heat treated)   15–16.5(depending on temper)

From Eq. (1), since beam deflection is a function of the beamdimensions, applied load and Modulus of Elasticity of the beam material,Eq. (1) can be restated as

$y = {{\frac{W}{192} \cdot K_{bf}}\mspace{14mu}{where}}$$K_{bf} = {{{Beam}\mspace{14mu}{Factor}} = \frac{l^{3}}{EI}}$

The beam factor K_(bf) is especially useful, since once a beam of almostany design has been determined to have a suitable deflection under load,an equivalent beam having the same beam factor can be designed to suitmanufacturing or other putter function purposes. For informationpurposes, the K_(bf) of a 6061-T5 aluminum beam, clamped at both endswhich is 3.500 inches long, 1.00 inches high and 0.100 inches thickequals 0.049.

Using this K_(bf), examples of equivalent fixed end beams 3.500 incheslong that would have the same deflection under load include a roundcylindrical beam with a 0.203 inch diameter, a square beam with sidesequal to 0.178 inches, and a beam whose cross section is an isoscelestriangle with a height of 0.866 inches and a base width of 0.260 inches,among many other possible designs.

Additionally, the beam may be constructed of an alternative materialwith a different Modulus of Elasticity. Once again, it is necessary torecognize that any prototype or modification to a design previouslyfound conforming is subject to USGA review in order to ensure that anysuch changes or unforeseen deviations in the manufacture of productionclubs does not deviate from designs previously found conforming. Thedimensions of this beam can be calculated using the K_(bf) previouslydetermined for 6061-T5 aluminum whose E has been taken as 10.5(10⁶)pounds per inch², but correcting for the new Modulus of Elasticity. Forexample, if the new beam is constructed of stainless steel with an Eequal to 28(10⁶) pounds per inch², the E ratio of these materials equals2.67. Changes may be made in the beam length l, beam width b, beamthickness d, or any combination of these. If it is assumed that the beamlength and width remain constant, it can be seen that an equivalent 303stainless beam would have the same K_(bf) if the beam thickness equaled0.072 inches, and would therefore have the same deflection under load asthe 6061 aluminum beam. While this beam may also be estheticallydesirable, the main reason to consider alternate beam length, width andthickness dimensions as well as the material used is to enableadjustment of the beams characteristic time in order to achieve thegoals of the beam concept.

It is important to note that when a shaft adapter is attached to thebeam, the deflection under load is reduced due to the increase instiffness provided by the shaft adapter.

While it is possible to develop the equations for calculating beamdeflection under this circumstance, it is also possible to provide thisinformation by testing a sample beam with a shaft adapter (or equivalentstiffening plates) attached to a beam and measuring the deflection underload. The percentage reduction in deflection under load can then be usedas a multiplier to modify K_(bf), and alternate beam designs asdescribed above can be established.

Also worth noting is that while the beam formula described above refersto beams with uniform cross sections, it is also possible to utilizebeams that do not have uniform cross sections.

While it is possible to develop the equations for calculating beamdeflection under this circumstance, depending on the complexity of thebeam, estimates of a composite moment of inertia value for the beamusing the same method described above may be more convenient.

What is most important to recognize is that the beam shape may be almostany design that meet the rigidity requirements of the USGA and which donot introduce nonconforming features.

Empirical Testing

In order to validate the effectiveness of the beam design of theinvention, a putting table was constructed to test the effects ofputter-ball impacts which were 0.5″ and 1.0″ from the sweet spot towardboth the toe and heel of the putters tested. A putting table rather thana typical practice putting green was desirable due to the unavoidablepresence of artifacts in any green that could introduce significanterrors distorting the results. In addition, putting from the same spoton the same line introduces a channel in the green, disturbing theresults.

The table constructed was approximately 22″ wide by sixteen feet long.The table base consisted of a parallel pair of sixteen foot long nominal2″ by 4″ wooden runners selected for flatness and straightness,connected to each other by five cross struts spaced approximately fourfeet apart. The runners and struts were positioned so that the 4″dimensions were vertical. Also, the cross struts were fastened so theirtop surfaces were approximately 1/32″ below the top surface of therunners to allow for providing a small recess running down the sixteenfoot length of the table when a pair of two foot by eight foot sheets of½″ thick underlayment plywood with one side finished was screwed to thetable base. In addition, five leveling jacks were positioned in each ofthe sixteen foot runners to provide for leveling of the constructionboth before and after the underlayment was added, to compensate forsubfloor, table base, and underlayment layer unevenness, as well as toallow for tilting the table lengthwise to provide the ability tocalibrate the Stimpmeter speed of the table. The height of the levelingscrews were adjusted for a truly horizontal (within the limits of thelevels utilized) surface both across the width and length of the table.

Once the table was constructed, two coats of vinyl-concrete cement wereskived down the length of the table to provide a reasonably flat surfaceacross the width and to minimize any irregularities in the underlaymentboards. After sanding, two layers of a rubberized vinyl elastomericcaulking compound were skived onto the vinyl-cement layer followed bytwo additional layers of a self-leveling thick rubber-acrylic paint thatwas similarly skived down the length of the table to provide a softersubsurface. Golf balls were manually rolled down the table length andacross the width to insure there were no significant artifacts presentand two layers of 1/16″ thick felt were stretched and stapled across thewidth and down the length of the table. A pair of ⅛″ thick by 1½″ wideby sixteen feet long wood strips were attached at each side of the tableas buffers running lengthwise and another crosswise at the end of thetable to prevent balls from running off the table at the sides or theend during testing.

It was found that when the table was truly horizontal across both widthand length, the Stimpmeter speed of the table was over fourteen feet.The table was then tilted by making use of the leveling screws so testputts ran uphill. In order to arrive at the target Stimp speed, it wasfound that a table slope of approximately 0.7 degrees (approximately a2⅜″ rise in the 16 foot length) was necessary.

Finally, in order to measure travel length and ball position, a metaltape measure was permanently attached on top of the wooden buffer stripalong the right table edge running its full length, while an aluminumdimensional T-square was used to determine ball location from the leftedge of the table.

Also constructed was an apparatus that would provide a calibratedpendulum stroke to a wide variety of putters. In order to eliminate thedamping and other effects of the grip, the clamp devised locked onto theshaft of the putter below the grip and was tightened to the same levelon all putter shafts. The center of the clamp was approximately 19″above the putting surface, but depending on the shaft position of someputters with a large face to back dimension, it required raising of theputter head slightly to prevent it from scuffing the table on thefollow-through of the swing, allowing the length of putter shafts tovary somewhat. It was also found that in order to prevent a swing strokefrom the inside, it was necessary to very accurately level andhorizontally clamp the pendulum shaft to which the putter clamp wasattached. Adjustments to putter balance were provided by balancingweights so that the putter face would impact the ball when the face ofthe putter was at its lowest position (the projection of the shaft on aplane perpendicular to the putting surface and parallel to the swingplane being vertical) in all cases in order to provide comparableresults.

With the shaft completely vertical and at rest, the ball was placed onthe table approximately 1/32- 1/16″ in front of the putter face. Twelvetests were made at five face locations, i.e. the sweet spot, ½″ and 1″towards the toe and ½″ and 1″ towards the heel. Each putter was adjustedso the ball would travel an average of ten feet, +/−2″ when impacted onits sweet spot. This was accomplished by increasing or decreasing thearc the pendulum shaft was allowed to rotate through by adjusting a stopto meet the ten foot +/−2″ travel average when tested at the sweet spotof each putter. This arc was held constant throughout the entire testsequence for each putter. Offline deviations were then calculated bymeasuring the distance between the average sweet spot location on the xaxis, while distance deviations were measured from the same sweet spotlocation on the y axis.

Prior to formal testing, it was noted that slight variations in the truelocation of the center of mass of the test balls could have asubstantial effect on ball travel distance and line. As a result, amotorized ball spinner was used, without success, to locate a greatcircle through the true center of mass and the theoretical location. Inaddition to finding non-repeatable locations of the dot and great circlelocations, it was difficult but necessary to align the great circleplane exactly vertical and on the putting line during test runs.

Also evaluated was the floating ball technique, wherein a dot is placedon the top surface of a ball barely floating to enable location of theexposed surface precisely. This positioned a great circle through boththe actual center of mass as well as the theoretical center, althoughmarking it, except for the floating dot, was not necessary. When themarked dot on the topmost surface of the ball was used to position theball in front of the putter face, the ball could be rotated horizontallythrough 360 degrees, so that it was not necessary to position a specificgreat circle directly over the putting line. Nevertheless, in order toposition the test ball so it was properly positioned with regard to theintended impact spot on the putter face and orientated the same way foreach putter undergoing test, the selected ball was marked in this mannerand, additionally, an arrow was placed on the great circle identified soall test putts were made using the same ball rolling in the top forwarddirection. Even so, some difficulties were encountered when it wasdetermined that, on rare occasions, an atypical error in ball locationoccurred. As a result, in all cases the two worst readings of the twelvetaken were eliminated, although in almost all cases, they were within orclose to the +/−2 Sigma target range.

Finally, in evaluating balls suitable for testing, it was found that twopiece balls came closest to meeting the necessary requirements, althoughseveral three piece balls were also found acceptable. For the purposesof the tests, a Titleist DT SO/LO®, was used for all the putters tested,keeping as close to the same orientation and direction of roll aspossible. The ball was retested several times using the floating balltechnique throughout the putter test cycles, without any noticeablysignificant changes developing.

A chart summarizing the results of the putting tests is set forth belowand FIG. 7 is a graphic illustration of these tests. A comparison of thetest results confirms the validity of the beam concept as originallyhypothesized.

SUMMARY OF PUTTER TESTS ON TEST TABLE DIRECTION--INCHES DISTANCE--INCHESDISTANCE BETWEEN SWEET SPOT AND HEEL SS TOE HEEL SS TOE Putter 1.0 0.50.00 0.5 1.0 1.0 0.5 0.00 0.5 1.0 1 3/32 BEAM −1.20 −0.24 0.00 +0.19+1.46 −5.42 +0.36 0.00 −0.53 −6.67 2 5/32 BEAM −2.35 +0.43 0.00 −0.33−0.83 −6.34 +0.55 0.00 −1.43 −6.31 3 7/32 BEAM −0.83 −0.70 0.00 +1.34+1.95 −7.19 −1.27 0.00 −2.52 −9.10 4 MALLET −1.85 −0.56 0.00 +0.22 +1.26−19.32 −2.52 0.00 −3.35 −13.14 5 HI MOI −1.96 −0.16 0.00 −0.60 +0.65−10.67 −1.07 0.00 −3.07 −13.07

Putters 1-3 are beam putters of the subject invention intended todemonstrate the effect of beam thickness. In all other respects, putters1-3 are identical, including the shaft and grip. Putter number 4 is avery popular mallet style putter which provides an elastomeric putterface. Putter number 5 is also a very popular high moment of inertiadesign which also contains an elastomeric face insert. Both wereselected to serve as base line putters against which beam putters werecompared on the basis of their performance reputation in PGAtournaments. In order to simulate blind testing as much as possible, rawtest data on all putters was collected prior to data analysis andreduction of this information to the differential measurements from thesweet spot is shown on the chart. It is worth noting that the shaft andgrips used on all three beam putters appeared to be the same as thoseused on putter number 4.

The results shown on the graphic representation in FIG. 7 are notsurprising in that the average ball centers for all five putters testedat all four (½″ and 1″ spacing, toe and heel) impact locations arewithin 2″ or slightly over 2″ from the sweet spot vertical axis. This isindeed the rationale behind high moment of inertia designs intended toreduce twisting of the putter head in order to keep the ball on or closeto the intended putting line. In the same sense, compression of anelastomeric putter face insert is intended to keep the ball in contactwith the putter face longer, allowing the putter face more time tosquare up in order to keep the ball on line.

What is of greater interest and importance is that when the impactlocation is at the ½″ toe or heel location for beam putters 1, 2, and 3,five of the six ball centers are inside a theoretical 4″ ball cupdiameter located at the sweet spot average location for that putter (thesole exception being the ½″ toe hit of beam putter 3); yet only one ofthe number 5 HI MOI putter balls is similarly located, and both of thenumber 4 putter hits at the ½″ toe or heel location miss the theoreticalcup diameter entirely. Nevertheless, it is important to note that on allfive putters tested, even those putts which do not reach the hole, theyare only about 1″ from the hole and are at tap in distance.

The same cannot be said for impacts which are 1″ from the sweet spot.While ball centers for beam putters 1 and 2 are between 3½″ and 4½″ fromthe cup edge, and beam putter 3 is somewhat further away at 5¼″ and 7″,putter 4 results are 11″ and 17½″ from the cup edge while putter 5results are 8½″ and 11″ from the cup edge.

These results clearly show the validity of the characteristic timeconcept of the beam putter design. As stated previously, energy storedin the deflection of the beam is recovered prior to impact and impartedto the ball as the ball leaves the putter face, providing improved ballroll distance, as well as maintaining optimum control of direction.

Additionally, it would appear that when elastomeric putter faces orinserts are employed, the characteristic recovery time may be so slow,the ball has left the putter face before the stored energy can bereleased to the ball, resulting in smaller ball travel distances onimpacts which deviate from the sweet spot. Similarly, when the putterface is all metallic, the only place where energy can be stored forlater release is in the ball itself. In this case, the amount of energythat can be stored due to ball compression as a result of a putt impactis so little, it may for all intents and purposes not have any effect onball travel. Finally, consideration of energy storage in the shaft asthe result of impact flexure shows that the characteristic recovery timeis so slow, the ball has also left the putter face long before thisenergy exerts any effect.

A similar analysis of putter impacts with regard to direction anddistance is contained in a book by Alastair Cochran and John Stobbstitled Search for the Perfect Swing, published by Triumph Books,Chicago. In one experiment which was performed, balls were impacted onthe sweet spot and 1″ in each direction towards the toe and heel using aconventional blade type putter. Balls impacted on the sweet spottraveled a distance of 11 feet, 2½″, while balls impacted 1″ towards thetoe and 1″ towards the heel traveled 9 feet, 0″ and 9 feet, 2½″respectively. These correspond to a differential from the sweet spottravel distance of approximately 24″ and are directly comparable to the11″ and 17½″ spacing found in the above test for putter number 4. At thesame time, Messrs. Cochran and Stobbs found that the offlinedifferential from the sweet spot were 8″ and 7″, corresponding to 6″ and5″ distances to the theoretical cup edge respectively for toe and heelimpacts, which are substantially larger than the differentials found forthe putters of the subject invention. Clearly, directional control issubstantially better for high MOI and beam putters as theorized.

While travel distances for a ten foot putt stopping two feet short ofthe hole are not considered tap ins, it would still be expected thatprobably 90% or more of these putts, depending on green conditions,would be sunk. On the other hand, if a twenty or thirty foot putt wouldstop four feet or six feet short of the hole, these would fall in therange that most golfers, including many professionals, would considertroublesome.

The conclusion to the above is that properly dimensioned beam putterswill not only adhere closely to the putting line, but if they areproperly optimized for the beam's characteristic recovery time, impactedballs would travel for a distance comparable to the sweet spot traveldistance, even when impacted as much as ½″ off the sweet spot.

Putt Distance Control

As has been shown empirically (see FIG. 7 and corresponding discussion)and as is known anecdotally, the further from the sweet spot the ballimpact location is, the shorter is its travel distance. Golfers facing adownhill putt have two choices. Either they can reduce the impact forceat the sweet spot, or they can purposely impact the ball close to thetoe of the putter face with the same force they would use as if theywere hitting a level putt for the same distance. This effect existsregardless of the MOI value of the putter in use, even though closeradherence to the intended putting line increases as the MOI of thespecific putter increases by weight disposition and even though the massof the putter remains constant.

This apparent paradox can be easily understood by making use of theConservation of Energy principle. The total kinetic energy of a putterat the instant before contact with the ball can be expressed as:KE _(p)=½m _(p) v _(p0) ² where m_(p)=putter mass and v_(p0)=headvelocity at time 0.

During the time period that the ball and putter face are in contact,energy is transferred from the putter to the ball. If energy loss due toball and/or putter face deformation are ignored along with other energyconsuming deflections (i.e. shaft, grip, etc.), and the impact locationis on the sweet spot, this can be equated as:Total KE=KE of the putter prior to impact=Residual KE putter+KE ball, orTotal KE=KE _(p)=½m _(p) v _(p0) ²=½m _(p) v _(p1) ²+½m _(b) v _(b1) ²where

v_(p1)=putter velocity=v_(b1)=ball velocity at time 1 when ball andputter face just separate.

However, when the impact location is not on the sweet spot, a turnproducing force is introduced around the center of mass of the putterhead. This is expressed as Torque=Fr=Iα where, as previously identified,F is the impact force, r is the distance from the center of massperpendicular to the impact force vector, I is the moment of inertia andα is the angular acceleration of the head.

For any value of T during the turning moment, higher MOI putter headsreduce the value of angular acceleration α, and subsequently ⊖, theincluded angle of rotation is lessened. Nevertheless, work is done bythe applied torque through this angle of rotation, and can be expressedas T⊖ since T⊖=(Iα)(w²/2α), or the kinetic energy consumed by the workof rotation of the putter head equals ½ Iw². As a result, the kineticenergy available to be transferred to the ball is less than thatavailable when impacted on the sweet spot and the ball.Total KE=KE of the putter prior to impact=½m _(p) v _(p1) ²+½ Iw ² 1/2 m_(b) v _(b1) ².

Since the value of kinetic head energy (½ m_(p)v_(p1) ²) available toimpact the ball is now reduced by the loss of rotational energy (½ Iw²),the resultant energy available to be imparted to the ball is reduced andthe ball travel distance will be lessened.

It is worth noting that while the included angle of rotation ⊖ would beextremely small with very high MOI putter heads, the total angle ofrotation of concern includes the torsional rotation developed by theputter shaft (quantified by shaft manufacturers as low, medium or hightorque shafts), the rotation in the grip due to its elastomeric nature,the rigidity of gripping the putter due to the strength of the handsgripping the club, as well as the elastomeric nature of the ball andputter head interface when an elastomeric insert is used on the putterface.

The conclusion to be reached is that even with very high MOI putterheads, many other independent and dependent variables contribute to theloss of energy that can be transmitted to the ball during impactresulting in loss of distance. The beam concept of this inventionprovides for storage of most, if not all of this rotational energy inthe deflection of a beam located between the hosel and the putter faceand which is returned to the putter face during the time the putter faceand ball are in contact, if the putter head has the propercharacteristic time. This greatly reduces any effect deflections of theshaft, grip and grip rigidity can introduce.

No other putter has, in the past or present, approached this level ofdistance control. While the claims of high MOI putter are correct inthat they more closely adhere to the intended putting line, high MOIputters do not, in of themselves, provide any active distance correctingfeatures, and as discussed below, high MOI putters result in a lowermagnitude of the sense of touch as it relates to feel, furtherexacerbating the problem of distance control.

Feel

A definition of the meaning of feel as it relates to golf has been aselusive as the search for a perfect ball or club. Indeed, the June, 2005of Golf Digest magazine is dedicated towards feel in all its aspects:tactile feel, kinesthetic feel, visual feel, intuitive feel, and soundfeel. With regard to the subject invention, these five kinds of feel areconsidered as follows:

1. Tactile fee, or the sensations perceived by the fingers or hands. Thesense of touch is as a result of impact.

2. Kinesthetic feel, or an awareness of what the body and club are doingduring the swing. This combines the senses of sight and time duringsetup and the swing prior to impact.

3. Visual feel, or the ability to see the swing/stroke as it is takingplace.

4. Intuitive feel, or the ability to imagine a shot before it takesplace. It is a combination of all the senses of touch, sight, sound andtiming as imagined mentally or in a practice swing.

5. Sound feel, as heard by the golfer during the swing or at impact withthe ball.

The first issue that has to be resolved is whether any of the sensesperceived during the putting stroke can have a cognitive or reflexiveresponse to alter the swing while it is taking place. Given that thecontact time of the putter and ball is typically in the range of 0.5-1.2milliseconds, and the time it takes for a signal from the brain to reachthe hands after receiving the stimulus is on the order of 10milliseconds (nerve travel speed is approximately 300 feet/second),cognitive feel for a response to the sense of touch is not possiblesince the ball is long since gone from the putter face. In the samesense, while a reflexive response to an impact with the ball mighttrigger a responsive reaction, it is not likely that the muscles in thearms or hands can respond before the ball is gone from the putter face.Even reflex actions require a muscle activation time.

Also, since the sound of the impact takes at least 2-5 milliseconds toeven be heard (the speed of sound in air is approximately 1087feet/second at STP), there can be neither reflexive nor cognitiveresponse to the sense of the sound of the impact that could have aneffect on the ball.

When considering the effect of the sense of sight to the putting strokefor both the kinesthetic and visual aspects, it is reasonable to expectthe complete take away and impact portion of a putting stroke to have aduration time somewhere between ⅛^(th) of a second and 3 seconds orlonger. If a visual input during the stroke indicates the club is not onthe correct putting line on either the takeaway or impact portions ofthe stroke, it is possible that a signal from the brain can reach thebody, arms, or hands quickly enough to alter the stroke, which implies acognitive response. While the responsive reaction may be beneficial,under or over correction is more likely, resulting in a wide range ofmishit responses, including short, long, pushed or pulled balls, andeven yips, and is clearly to be avoided. The implication is thatalignment (or aiming) of the putter consistent with the intended puttingline is significantly important at set up, the takeaway and the impactportions of the stroke.

Finally, the intuitive sense suggested is, in all likelihood, the mostimportant factor since it relies on the storage in the brain of inputsfrom all the active senses. For example, while practicing on a puttinggreen before a round, and assuming the Stimp speed of all the greens isconsistent, the senses of touch and sound translate to how much force isrequired for the ball to travel a given distance. These senses arestored in the brain for future recall during the round as are visual andtiming senses, all of which may be derived from both long and short termmemories.

The bottom line to putting feel is that a stroke delivered as intendedis the result of the integration of all the memories stored in the brainand their application as it applies to the stroke in question. It isreasonable to expect that anything that amplifies or modulates theintensity, frequency, or duration of the memory of these sensesstrengthens useful memory recall.

While the descriptions above constitute what is the generally acceptedphilosophy useful for establishing a putting technique, once the puttingline has been established, control of the distance the ball travels isthe most significant requirement for a useful putting stroke, and thegenerally accepted philosophy described above is not necessarily thebest possible technique.

Touch

The sense of touch refers to the signal created when pressure is appliedto most portions of the body. Some areas have a greater response thanothers, and the level of response of course varies between golfers.Nerve endings below the skin act as sensors which are chemicallyconverted and passed along for transmission to the brain. Note thatsensitivity refers to pressure, not force. This can be demonstratedeasily by rubbing the flat surface of a comb over a portion of the handswith a small force, following this by applying the same force but withthe points of the comb tines making contact. It is normal to find thatthe finger tips are relatively less sensitive to the contact than arethe palms of the hands. Much of this is due to the loss of sensitivityof the finger tips as a result of various degrees of abuse the fingershave been subjected to over time. Typical is the constant pressureapplied when simply using a writing instrument. This is unfortunate inthat it is the finger tips where the greatest pressure of an exertedforce can be sensed, while the more sensitive palms distribute theexerted force over a much larger area resulting in a lower pressure thatcan be sensed for transmission to the brain for analysis. For thisreason, many golfers grip the clubs in various ways to try and enhancetouch by contacting the club along the fingers or palms, as in the clawor other styles. Nevertheless, the ball and putter face impact forces asthey are generated can be analyzed to determine how they respond tovarious putter designs as they apply to the sense of touch. There aretwo forces which can be considered. These are:

a) The natural resonant frequency of the putter including the shaft andgrip.

b) The force transmitted by the ball-putter face impact travelingthrough the head and up the shaft.

With regard to a) it is believed that virtually everything has a naturalresonant frequency. This ranges from the earth itself having a firstresonance peak at about 7.8 Hz. (the Schumann resonance) to ocean waves,musical instruments, gongs, pipes, rods, liquids, atoms, and of coursegolf clubs. These natural resonant frequencies are a function of theirstructural materials as well as their physical shape.

The impact of the putter head striking the ball initiates two energywaves. These are the impact shockwave and the sound wave (discussedlater) at frequencies determined by the geometry and composition of theputter head and of the ball. Typically, while the shockwave energydissipates itself by friction within the atomic structure of the head asit ricochets within the club head, some of it will find its way up theshaft to the grip. Note that Huygen's principle of a shockwave emanatedfrom a point impact will radiate in all directions from the contactpoint and that the wave front is in phase in all directions as itradiates through the head until it impacts an interface and rebounds. Bylocating and measuring the magnitude of the shockwave up the shaft, thenode or point of maximum response can be determined.

While an accelerometer can be used to determine this location as well asthe shockwave frequency, a relatively simple observation of this can bemade by suspending the putter in a vertical position by holding it verylightly in the fingers of one hand near the bottom of the grip whilestriking the face of the putter with a ball in the other hand. Bychanging the suspension point by small increments up or down the shaft,the point of maximum vibration can easily be determined. Note that bysuspending and holding the putter with a string fixed at the butt end ofthe grip to minimize dampening, a much lighter force can be exerted bythe fingers making it still easier to sense. Also, holding it near anear at the node will enable the golfer to hear the sound wave set inmotion by the vibration of the shaft at this point for an estimate ofthe vibration frequency. Normally, the comparative magnitude of thevibration can be sensed by touch as well as by sound since the durationof the audible signal is typically 2-3 seconds or longer.

The distance between this point and the impact point with the ball is¼th the wavelength of the shockwave, and is approximately 2 to 2½ feetfrom the sole of the putter head for many putters with a shaft length of35″ and a head weight of approximately 350 grams. Thus the wavelengthwould be approximately 8-10 feet. The shockwave frequency can also bedetermined experimentally and typically appears to be on the order of15-35 Hz. From Eqs. (6) and (7) below, this equates to a shockwavevelocity of approximately 250 feet/second (approximately 0.5% of thevelocity of sound transmission in aluminum), and a period ofapproximately 40 milliseconds which is well past the point at which theball leaves the club face. Nevertheless, this is an importantobservation since it is the point where the fingers or palm should belocated to maximize the sense of touch of the impact which in turnprovides a measure of the impact force and which fundamentally is whatwe are interested in as a measure of ball travel distance.

(b) While the resonant frequency of the putter was determined above bythe initiation of a shock wave, it is of interest to consider themechanism by which the shock wave travels up the shaft. Any impact on asurface will produce a stress on both of the impacting members. In aputter, these stresses will strain the lattice structure of a metalputter face adjacent to the point of impact which in turn will transfersome of this strain to adjacent atoms making up the lattice structure.As was previously indicated, some of these strains will find their wayup the shaft and while some of the stresses will dissipate as frictionbetween atoms making up the lattice structure, the largest part of thestresses will be distributed as a flexure in the shaft and grip. Thesestresses can be, and in an impact that misses the sweet spot usuallyare, both linear and torsional. While these strains will absorb theforce of the impact and still exist long after the ball leaves theputter face, a significant part of them will travel up the putter shaftas a result of the kinetic energy the atoms acquire as a result of theimpact. The variables contributing to the transfer of this energyinclude both the independent and dependent variables previouslydescribed. As the strains and vibrations developed as a result of theball impact harmonically decay, they can be sensed by the golfer and areusually attributed by the golfer as a property of the putter. Mostcommonly, they are described as having a “hard” or “soft” feel, withlong decay times characterizing a “soft” feel. One must also recognizethat the character of the golf ball in use also has a major effect onthese properties.

While the errors introduced by differences in the absolute values ofthese variables can be analyzed from both linear and rotationalcalculations, visualization of these variables by their electricalanalogs can provide a clearer understanding. The following chartprovides the mathematical relationships between mechanical andelectrical analog parameters.

Nomenclature For Electrical Analogs V or E Voltage I Current Z ImpedanceR Resistance L Inductance C Capacitance X_(L) Inductive Reactance X_(C)Capacitive Reactance F Friction E Stored Energy f Frequency ω AngularVelocity (as in a stressed beam) in cycles/sec. in radians/sec. v Wavevelocity λ Wavelength p Period Mathematical Relationships (1) E = IZ (2)Z = {R² + (X_(L) − X_(C))²}^(1/2) (3) X_(L) = ω L (4)$X_{C} = \frac{1}{\omega C}$ (5) ω = 2 Π f (6) v = f λ (7)$p = \frac{1}{f}$

Electrical Analogs

The following analog equivalents are assigned to assist in understandingthe analysis that follows. Italics are used to distinguish betweenparameters employing the same font characters.

Mechanical Parameter Electrical Analog Impact Force F is equivalent toVoltage V or E Mass M ″ Inductance L MOI I ″ Impedance Z Friction F ″Resistance R Stored Energy E ″ Capacitance C Velocity V ″ Current I

While the electrical equivalents indicated are relatively simple tounderstand, it is worth noting that the reason that I is the analog forV derives from the fact that current is the transfer of charge (Q) as afunction of time.

$I = {{\frac{\mathbb{d}Q}{\mathbb{d}t}\mspace{14mu}{just}\mspace{14mu}{as}\mspace{14mu} V} = \frac{\mathbb{d}s}{\mathbb{d}t}}$

When the putter strikes the ball, the force F can be equated to voltageV, the magnitude of which is proportional to the force of impact. Thisinitiates a shockwave energy pulse which is dissipated by the frictionof atoms rubbing against each other as the pulse travels through thehead. In a DC relationship, Ohms Law (I=V/R) is the electrical analogfor V=F/F, where V represents the velocity of the shockwave force F asit dissipates its energy as friction F. Since it is obvious that theshockwave F is not a single pulse, but travels at a wavelength aspreviously described and which is a function of the geometry of theputter head, this analysis can be continued as an alternating currentanalog I whose frequency is determined from the shockwave velocity. Whatis significant is its relationship to the touch sense of feel. Theshockwave impulse is not a square wave but builds up and decays as afunction of the Young's Modulus of the impact interface materials. Forsimplicity, the shockwave can be considered to have the general form ofa sine wave.

From Eq. (1) the electrical analog E=IZ and Eq. (2), orE=IZ=I{R²+(X_(L)−X_(C))²}^(1/2) it is clear that as R and/or X_(L)increase so does Z, and I must decrease. Since Z is the electricalanalog for the moment of inertia, an increase in Z is the equivalent ofan increase in MOI. Translated to its mechanical equivalent, this meansthat the magnitude of the mechanical pulse V reaching the shaft of theputter is reduced, resulting in a smaller sense of touch as it appliesto the magnitude of the impact of the putter face and the ball that isavailable for the sense of touch to recognize. It is interesting to notethat in an electrical circuit, an inductance L is referred to as a“choke”, indicating its effect in reducing the flow of current in thecircuit, or as its mechanical equivalent, the magnitude of the impact ofthe putter with the ball.

Stated in simpler terms, the significance of this is that the higher themoment of inertia, the lower is the overall feel provided by thereduction in the magnitude of the sense of touch.

On the other hand, from Eq. (2), there is an optimum value of X_(C)where X_(C)=X_(L) and the total reactance equals zero, the value of Ibecoming a function of the resistance R only. Translated to itsmechanical equivalent, this means that the magnitude of the shockwavepulse V as expressed by its electrical analog I reaching the shaft ofthe putter must increase, resulting in a larger feel for the impact ofthe putter face and the ball that is available for the sense of touch tobecome aware of.

Again stated in simpler terms, the significance of this is the energystorage provided by the putter beam (whose electrical analog is thecapacitor) results in a decrease in the moment of inertia and anincrease in the overall feel provided by the accompanying increase inthe magnitude of the sense of touch. There is an optimum value of aputter's moment of inertia for both accuracy and the sense of touch asit relates to feel. Putters with moments of inertia between 2000 and8000 gram·cm² are contemplated.

Sound

The velocity of sound generated and transmitted within the club head isentirely a function of the club head material. For information purposes,the longitudinal speed of sound in brass, aluminum and steelrespectively are approximately 15,400, 21,050 and 19,000 feet/second,while the transverse speed for these materials are approximately 6925,9975 and 10,175 feet/second. At STP, the speed of sound in air is only1087 feet/second. The frequency of the sound wave is determined by boththe geometry and material of the club head resulting in vibration of thesurface atoms of the putter and producing an audible sound. Obviously,the net speed of sound transmission is a function of the combination ofboth longitudinal and transverse wave transmission, thereby puttingHuygen's principle in perspective. Putters typically have a soundfrequency ranging between 10-3000 Hz.

As was noted previously, everything, including atoms of materials, has anatural resonant frequency. As was assumed in the previous electricalanalog analysis that a sine wave was responsible for the transfer ofenergy, sound waves also travel as sine waves but their origin is alittle different. The impulse shock wave developed on contact with theball cannot be a truly square wave since both the ball and putter facesare each elastic materials with a Modulus of Elasticity specific to thematerials being used. It follows therefore that deformation of bothmaterials occur at the interface, and that increasing compression occurson impact over time. It is also reasonable to believe that constantmaximum compression will exist for some finite time duration, followingwhich compression is lost as the ball starts to leave the putter face.The shape of the force curve during the rise and the fall times as theball leaves the putter face is a function of the impact force as well asthe materials of construction and can be determined by use of anoscilloscope if desirable. Despite the above analysis, it is necessaryto bear in mind that the total time the putter face and ball remain incontact during a putt has been measured to be between 0.5-1.2milliseconds. Typically, less than one thousandth of a second, and theaudible component of the sound generated has not yet traveled ⅓ of thedistance to the golfer's ears.

Whatever this single pulse wave shape is, it can be simulated by Fourieranalysis into a series of overlapping half sine waves that, in sum,duplicate the wave shape of the impact force. Since several of thesehalf sine sound waves will be at a frequency close enough to theresonant frequency of any atom it may strike, reinforcement will occurif it arrives in phase. By adding its kinetic energy to the energy ofthe atom's natural resonant frequency sine wave, the atom's potentialenergy is increased, and which in turn is converted to a higher energyfull sine wave as the potential energy is recovered. This in turn causesother atoms in the putter head to higher peak magnitude levels as energyis transferred to other atoms throughout the head. This includes theshaft unless its path is restricted from transferring its vibration bythe mechanical structure of the putter head or by some other means ofdamping. While much of the impact energy is lost in friction betweenatoms, once the atoms on a free surface are set into vibration, ittransfers this wave motion to air atoms adjacent to the putter freesurfaces and the characteristic sound of the putter impact is perceivedby the golfer's ear.

It is important to recognize that shaft location in the head plays asignificant role in the frequency and magnitude of sound produced. Thiscan be demonstrated by using a wine glass as an analogy. If the wineglass is held by its base and the bowl portion of the glass is struck,the vibrations generated will set air atoms adjacent to both the insideand outside of the bowl in motion. The observed frequency will be afunction of the tuned column of air on the inside of the wine glass bowlmodified by the harmonic generated by the outside of the glass couplingto exterior air atoms. If the wine glass is grasped by its stem and thecup struck, little variation in sound frequency and/or magnitude will besensed. This remains true even though the stem may be grasped very closeto the bowl. If the cup is touched while it is vibrating, it willimmediately be damped and the frequency, magnitude and vibrationduration will be greatly reduced. Continuing, if the wine glass isgrasped by the bowl and struck, all that generally can be heard is adull thump. The point is that damping is a critical factor in the soundproduced, and the narrow diameter stem serves to isolate the vibrationwave from the damping effect of the stem holder.

If this analogy is applied to a putter, it is apparent that the wineglass stem represents the shaft of the putter while the bowl representsthe putter head. If reference is made back to the electrical analogydeveloped for the analysis of the force wave transmitted to the hand, asimilar analysis shows that the impedance of the stem, which is mainlyresistive, blocks most of the force wave from reaching the hands. On theother hand, touching the bowl of the wine glass increases the mass ofthe system and the result is an increase in the moment of inertia, themajor effect of which is the damping of the bowl's vibration. Increasedmass also equates to a lower resonant frequency for a wine glass of thesame size and shape but with a higher glass density.

These observations also apply to the observed frequency of a putter.Isolation of the shaft from the vibrating head will result in a higherresonant frequency and a longer duration of vibration, both of which areimportant contributors to the overall feel provided by sound, and alsothe implied sense of “time”. The frequency and duration of the impactsound is important in that the larger the magnitude that can beperceived is, the stronger is the stored memory. This is important inthat it is easier to distinguish a small change in level when the baseline of comparison is large rather than small. For example, if theinformation stored in memory of an impact is five seconds long, animpact sound duration of one second will easily be identified. On theother hand, if the duration stored in memory is approximately 1.5seconds long, an impact duration of one second could barely bedifferentiated. Since the duration of the impact sound wave is a measureof the force applied for a given putter, it is not only a significantcontributor to the concept of “feel”, it is in fact a much largercontributor than the sense of touch.

In order to follow the reasoning behind the importance of the impactfrequency, one must recognize that sensitivity to hearing differentfrequencies varies from person to person. In fact, the well knownFletcher-Munson and Robinson-Dodson equal loudness curves indicate thatfrequencies between 1000 and 4000 hz. are more easily heard by mostpeople than frequencies at lower or higher frequencies. This of courseis what leads to bass and treble boost for high fidelity music responsein an attempt to have all frequencies perceived by listeners to be atthe same loudness level of hearing for flat response. The impact soundfrequency of between 1000 to 4000 hz. is also considered the applicablerange for which most golfers have the greatest sensitivity.

In an experiment to evaluate the vibration damping of the beam putter ofthe present invention, as a result of the beam and its connected shaft,a frequency measurement of the sound was made as a result of the ballimpact, and was determined to be approximately 1400 Hz. The beam wasthen severed from the head at the point where it was connected, and thehead was suspended by several strings so that it was disposed in atypical putting orientation. A ball was then allowed to impact theputter face close to the putter's sweet spot. There was no discernibledifference in the frequency of the impact sound at any impact forceattempted. It was also clear that both the magnitude of the sound andits duration were both a function of the impact force. With regard tothe frequency for the design tested, only one test observer felt that itwas somewhat harsh, and indicated he preferred a slightly lowerfrequency. This person also indicated that after he used the putter on atest green for a while, he “got used to the sound”. It is worth notingthat several methods of altering the sound frequency can be employed,including dimensional and material modifications. An estimate of soundfrequencies that would provide the benefits of discernible soundmagnitudes and durations that would be most widely acceptable is at thelower end of the equal loudness curves described above. In this regard,the vibration of the original Ping Solheim putter, U.S. Pat. No.3,042,405, has been described by many users as disconcerting, eventhough it is within the equal loudness curves described above, butcloser to the higher frequency end.

Putter Head and Putter Face Design

The beam concept of this invention can be included in virtually anyputter head design. All that is necessary is that there be clearancecompletely around the beam and shaft connector, except at the beam ends,as is depicted in FIGS. 2 and 8 a-8 d.

In FIG. 2, the top view of a preferred head design, the dimensionspreviously described are typical and for reference only to showcompliance with USGA requirement. The large clearance between thebeam-shaft connection at central beam section 34 and wall members 14 and18 allow for adjusting the moment of inertia to a desired value simplyby adding or deleting material to these outside wall members.Additionally, the harmonic oscillation decay of beam 30 from face 10towards the back of the putter suggests the placement of groove 42 andarrow 44 on the connection at central beam section 34 and similarlyshaped arrow 46 on back section 45. Groove 40, also on back section 45,representing the sighting line for both the forward direction and stanceset up, as well as arrowed section 41 cited directly above the puttingline and pointing in the direction of the takeaway stroke, providevisual aids in adjusting the swing to suit the recommended technique. Asdiscussed previously, back section 45 permits easy adjustment of face toback balance by the removal or addition of weight to weight balance port17. Finally, replacement of the connection at central beam section 34 asan assembly to provide for both a desirable characteristic time and beamshape, can be facilitated in the initial manufacturing process as wellas in field replacement, provided a proper replacement tool isavailable. The latter requirement must meet USGA requirements to preventsuch replacement during a round.

FIG. 8 a is a top view of head 70, a simplified version of FIG. 2, basedon a segment of a circle where the face of the putter is a chordselection to provide the shape and length of the putting face. FIG. 8 bis a top view of head 71, a rectangular shaped head, similar to a bullseye putter, which provides putting faces on both the front and backfaces of the head. FIG. 8 c is a top view of head 72 in a three sidedconcept, into which many of the features described for FIG. 2 may beincorporated. FIG. 8 d is a top view of head 73, except that the onlyopen areas in the head are those required to provide clearance aroundthe beam and its shaft connector, allowing the beam to function asrequired. This is essentially a mallet putter design.

The head designs shown in FIGS. 2 and 8 a-8 d are only to be consideredexamples of the use of the beam technology of the invention and are notexclusive to these putter head designs. It is contemplated that otherequivalent designs using the beam concept are within the scope of thisinvention.

As with putter head shapes, various putter face configurations can beutilized with beam putters of the present invention. For purposes ofexample only, three such faces are shown in FIGS. 3, 9 a and 9 b. FIG. 3is a normal face 10 wherein the height of the face is consistent withthe height of the putter body, as described previously.

FIG. 9 a depicts putter face 75 that is useful for plumb bobbing inaccordance with U.S. Pat. No. 6,358,162. When the putter is suspended bythe shaft, top surface 76 of putter face 75 is truly horizontal andprovides a ready reference to estimate slopes around the hole andelsewhere on the green. In this design, weights are strategicallydistributed (or eliminated) around the head to provide toe to heel andface to back balance in order for the putter shaft to hang in a trulyvertical alignment.

FIG. 9 b depicts putter face 77 a variation of FIG. 9 a wherein theshaft will hang in a truly vertical alignment as a result of thesymmetrical weight distribution from toe to heel around each side of thevertical axis of the center of mass. Depending on whether the putter isdesigned for righthanded or lefthanded golfers, the top surfaces of theportion of the face towards toe 78 (left portion for righthanded golfersor the right portion for lefthanded golfers in the drawing shown) willbe aligned as a truly horizontal reference as viewed in FIG. 9 a.Depending on the head design, weight may be required in the sideopposite the face to provide face to back balance.

As previously described, many beam materials, shapes and designs may beused to obtain the characteristic time desired. As a result, the abilityto easily substitute different beam members is important. While manydesign concepts are available, FIGS. 10 and 11 a-c show a simple versionof such a design connection between a beam member and perimeter wallmember of the putter head. Removal and reconnection of beam members mustalways conform with USGA requirements.

FIG. 10 is a close-up view of the beam to perimeter wall memberconnection. During manufacture, slots 80 are machined into perimeterwall member 16 where the ends of beam section 32 would normally belocated. Slots 80 are shaped to suit beam ends 32 a and extend abouthalfway into perimeter wall member 14, as shown in FIGS. 11 a-11 c,stopping short of the putter sole. Beam section 32 is stepped at 82, thebottom of its ends, so that when inserted into slots 80, the beam comesto a positive stop. Hole 84 is drilled to accommodate a properly sizedbolt, stopping just short of the depth of slot 80, whose diameter issuch that a small amount of material is also removed from ends 32 a ofbeam section 32. Hole 84 is then tapped to provide clamping of beamsection 32 to perimeter wall member 14 with bolt or screw 86.Alternately, the portion of the beam which is inserted into the body maybe of a different shape than the beam, such as a larger shape withtapered sides matching slots in the body, which would provide moresecure clamping capabilities.

This design concept can also be utilized by providing a replaceableshaft connector for beam sections 32 and 36 in central beam member 34.Beam sections 32 and 36 are attached to beam member 34, by providingslots 90 and 92 in the central beam member 34 into which the beamsections are inserted. FIGS. 13 a-13c show this connection, with holes93 and 94 tapped between beam sections 32 and 36 and central beam member34. Again bolts or screws 95 and 96 are inserted in holes 93 and 94 tosecure the connection.

The connection designs shown in FIGS. 10, 11 a-11 c, 12 and 13 a-13 cmake it possible to utilize beams and shaft connectors of many differentmaterials and designs, demonstrating that different connectionconfigurations may be employed which incorporate the beam concept.

Sighting Alignment

Failure to follow the intended putting line during the putting strokemay result in a mishit, since a visual signal to the brain that theputter is off line can initiate a cognitive signal to correct theproblem. There are two principle causes of off line swings:

1. Misalignment of the club with the intended putting line during setup.

2. Deviation of the club from the intended putting line during theswing.

It is generally recommended that when lining up a ball to be putted, thegolfer should position the ball close to his front foot with his/herleft eye (for a righthanded golfer) directly over the ball or slightlycloser to his/her foot than the ball. Most putters have an alignmentmark on the top surface of the putter directly above the sweet spot onthe face of the putter when the putter is properly soled. When theintended putting line is determined, the putter face should be lined upperpendicular to the intended putting line with the alignment markdirectly in back of the ball and also on the intended putting line. Fora righthanded golfer whose dominant eye is also the right eye, thisplaces the sighting eye, the alignment mark, and the ball in a straightline for viewing the ball path on the intended putting line. Thefundamental problem occurs in the difficulty in placing the dominant eyeproperly and there are many putters which use arrows, balls or othermeans of positioning the eye properly. Although the direction and path aball will take is primarily a function of the swing path (outside in, online, inside out, or parallel to but off the putting line), it is theaiming of the putter face square to the intended putting line when theputter impacts the ball which can introduce or exacerbate an error ineach of the swing paths described. One thing is clear. Unless the putterface is square to and the sweet spot is on the intended putting line,starting with a built in error only complicates the putting swing.

While many teachers understand the importance of the dominant eye beingproperly in line with the putting line, it is curious to note that someteachers ascribe a ball path when struck inside the intended puttingline being at least partially due to the dominant eye being inside theintended putting line at setup. Others cite the reverse, saying a pulledputt is due to an outside in swing, ignoring the issue which is properlyaiming the putter face to be square to the putting line at both set upand at impact. While all acknowledge the importance of proper alignmentat set up and at impact, it is clear that a proper understanding isrequired of how significant the location of the dominant eye is inrelation to the intended putting line.

Assuming that the path of the putter is on the intended putting lineduring take away and the impact portion of the stroke, (i.e. there is norotation of the wrists either opening or hooding the club face), ballswhich are pulled or pushed as a result of what may be considered aperfect swing can only be due to the face of the putter being improperlyaligned during set up. Keep in mind that a face which is out of squareto the intended putting line by only 1 degree will result in being over3 inches offline (enough to miss the edge of a hole) only 15 feet away.Yet most golfers find it difficult to discriminate an angle within 2 or3 degrees of being square to the putting line, which in the absence of aguide, is a mental image. For this reason, many golfers try to select aspot 5-15 inches ahead of the ball and aim the alignment mark at thatspot during set up. FIGS. 15 a-15 c illustrate how improper location ofthe dominant eye can easily introduce an error of 3 degrees or more ofthe putter face being out of square with the intended putting line atset up.

FIG. 15 a illustrates putter 102 lining up ball 100 for a putt alignedwith dominant eye 104 and left eye 106 as is generally recommended. Notethat visual sight line 108, intended putting line 109, dominant eye 104,left eye 106, alignment mark 110, and putting line target 112 are all ona straight line.

FIG. 15 b illustrates the same conditions as FIG. 15 a, except that bothdominant eye 104 and left eye 106 are positioned approximately ½ inchinside intended putting line 109 (closer to the golfer's feet). Notethat when dominant eye line of sight 108 passes through alignment mark110, the visual sight line passes well above (outside) of putting linetarget 112.

FIG. 15 c illustrates the golfer's actions to correct this. Toaccomplish this, the golfer intuitively rotates putter head 102, whiletrying to keep dominant eye 104 in the same relative position. This maybe accomplished by rotating the shaft, changing the grip position, or byrepositioning the feet or body which would move the grip location, shaftand/or dominant eye location. New visual sight line 114 and intendedputting line 109 will, in the golfer's mind, now line up properly witheach other, however the face of putter 102 is now closed to the intendedputting line. Depending on whether putter head 102 stays on intendedputting line 109 or is struck on an outside path, ball 100 in both caseswill result in travel path 116 to the left of target 112.

Note also that in order to minimize this problem, many golfers positiontheir left eye and dominant eye further back than is generallyrecommended, increasing the distance from their dominant eye to thealignment arrow. This decreases the error angle and once the puttingline is established, the golfer repositions his feet to whatever isnormal for him.

In order to more accurately position the dominant eye directly over theintended putting line, the present invention provides a sightingalignment groove or slot in the top surface of the putter head. Byproviding one or more strips of a contrasting color on the base of theslot, one can determine whether one's dominant eye is properly centeredover the intended putting line. Either a part of or all of a slot willbe obscured if the dominant eye is not properly positioned.Additionally, if the dominant eye is positioned back of the putter head,any rotation of the putter head off line will similarly obscure a partof one or more of the contrasting sight lines.

For example, sighting alignment slots or grooves 40, 42 and 48 have anexemplar width and depth of approximately ¼″, formed within crownsurface 9 of putter head 4. See FIGS. 16-18. Grooves 40, 42 and 48extend from face 10 to back end 22, each groove having substantiallyvertical (as shown in the figures) or tapered sides of approximatelybetween 0-10 degrees. The grooves are perpendicular to the face of theputter and are positioned directly above and parallel to the center ofmass and the sweet spot so that they can be positioned directly over theintended putting line when the putter is properly soled on the puttingsurface. Base surfaces 43, 45 and 51 of grooves 40, 42 and 48 areprovided with one or more stripes of contrasting colors, so the golfercan determine whether his or her dominant eye 104 is properly locateddirectly over the grooves and centered over intended putting line. Whenproperly centered all stripped, colored areas of the bases are visibleto the golfer. If the dominant eye is not properly positioned, allstripes cannot be seen. See FIG. 18.

FIG. 19 a shows the sighting alignment grooves of the present inventionin use with a standard mallet putter. Putter head 120 comprises groove122 with base 124 having one or more stripes of contrasting colors.Dominant eye 104 and putter head 120 are aligned on intended puttingline 109 and line of sight 108. All stripped colored areas in groove 122are visible and putter is properly aligned.

FIG. 19 b shows putter head 120 aligned on intending putting line 109,but dominant eye 104 is below the line, closer to the golfer's feet. Inthis case, line of sight 108 intersects with the top of groove 122 atpoint 130. Every part of groove 122 above line of sight 108 is clearlyvisible, since groove walls are not obscured. At point 130, everythingbelow line of sight 108 to the left of point 130, cannot be seen ifwithin groove 122.

FIG. 19 c presents the situation in which dominant eye 104 is close tothe ground. Everything below line of sight 108 to the left of point 140cannot be seen if within groove 122 and between the line of sight andlower image line of sight 142. Dominant eye 104, intended putting line109, line of sight 108, alignment mark 110 and center of ball 100 allcoincide, but the axis of the head is askew. However, since the golfer'seye is well above putter head 120, it is difficult to determine whenthis situation exists. Although uncommon, this occurs when the golferlowers his head and dominant eye until it is very close to the ground.Alternatively, standing back of the ball and holding the putter head ateye level and parallel to the putting surface, the golfer can align theintended putter line, the ball, and the line of sight. Thisautomatically squares the putter face to the intended putter line. Byselecting a point in front and back of the ball, the golfer can positionthe putter properly. In addition, a mental image of the putter face toeand heel can act as a t-square to aid in positioning the putter.

Certain novel features and components of this invention are disclosed indetail in order to make the invention clear in at least one formthereof. However, it is clearly to be understood that the invention asdisclosed is not necessarily limited to the exact form and details asdisclosed, since it is apparent that various modifications and changesmay be made without departing from the spirit of the invention.

1. A golf putter having a shaft and a putter head, said putter headcomprising: a body having a front member with a putter face having asweet spot to be aligned with a desired putting line and a rear section,perimeter wall members connected to and extending from the putter faceto the rear section of the body, an opening within and extending throughthe body, said opening being bordered by and enclosed within the frontmember, the perimeter wall members and the rear section, and an activelycompliant beam member extending parallel to the putter face of the frontmember and being particularly configured to deflect upon putter faceimpact with a golf ball, the deflection of the beam member being greaterthan the golf ball impact deflection of the putter face, said beammember being located within and extending uninterrupted completelyacross the entire length of the opening, the beam member being securedto the putter head solely by connection directly to the perimeter wallmembers and means for attaching the shaft directly to the beam member ata location between the perimeter wall members, whereby golf ball impactupon the putter face causes deflection of the beam member resulting inmaintenance of the orientation of the putter face with respect to theputting line.
 2. The golf putter as in claim 1 wherein the beam membercomprises a central member interconnected between two lateral beammembers.
 3. The golf putter as in claim 1 wherein the beam membercomprises a single beam extending between the wall members.
 4. The golfputter as in claim 1 whereby the shaft is attached at an angle greaterthan 10 degrees from a vertical plane.
 5. The golf putter as in claim 1wherein the body includes two perimeter wall members.
 6. The golf putteras in claim 1 wherein the perimeter walls comprise a rearward sectionand a forward section and the beam member extends between thesesections.
 7. The golf putter as in claim 1 wherein the putter has acenter of mass and the putter face has a sweet spot, whereby uponapplication of a momentary impact force offset from the sweet spot, atorque is produced about a fixed axis through the center of mass of theputter, the beam member producing a counter-torque when the impact forcebegins to decrease.
 8. The golf putter as in claim 1 wherein the putterface has a sweet spot to be aligned with a desired putting line, wherebythe impact between a golf ball and the putter face at a location offsetfrom the sweet spot results in deflection of the beam member followed bysubstantially simultaneous recovery of the beam member, causing theputter face to return perpendicular to the desired putting line atalmost the same instant the golf ball leaves the putter face.
 9. Thegolf putter as in claim 8 wherein the deflection and recovery of thebeam member to cause the putter face to return to the desired puttingline is the characteristic time of the beam member.
 10. The golf putteras in claim 1 further comprising means to connect the beam member to thewall members to allow removal and reconnection of the beam member oralternate beam members to the wall members.
 11. A golf putter having ashaft and a putter head, said putter head comprising: a body having afront member with a putter face having a sweet spot to be aligned with adesired putting line, a rear section, perimeter wall members extendingfrom the putter face to the rear section of the body, and activelycompliant beam means for correcting golf ball mishits upon golf ballimpact with the putter face, the beam means being particularlyconfigured to deflect upon putter face impact with a golf ball, thedeflection of the beam means being greater than the golf ball impactdeflection of the putter face, whereby the impact between the golf balland the putter face on the sweet spot results in deflection of the beammeans in proportion to the force of the impact while maintaining theputter face orientation with respect to the putting line at almost thesame instant the ball leaves the putter face, and is followed by beammeans recovery from the deflection, said beam means recovery directlyaffecting the angular orientation of the putter face in order to correctgolf ball mish its by causing the putter face to return perpendicular tothe desired putting line at almost the same instant the golf ball leavesthe putter face, said beam means being positioned parallel to the putterface and being located rearward of the front member and extendinguninterrupted between and connected directly to the perimeter wallmembers, and means for attaching the shaft directly to the beam memberat a location between the perimeter wall members.
 12. The golf putter asin claim 11 wherein the beam means comprises a central memberinterconnected between two lateral beam members.
 13. The golf putter asin claim 11 wherein the beam means comprises a single beam extendingbetween the wall members.
 14. The golf putter as in claim 11 whereby theshaft is attached at an angle greater than 10 degrees from a verticalplane.
 15. The golf putter as in claim 11 wherein the body includes twoperimeter wall members.
 16. The golf putter as in claim 11 wherein theperimeter walls comprise a rearward section and a forward section andthe beam means extends from these two sections.
 17. The golf putter asin claim 11 wherein the putter has a center of mass, whereby uponapplication of a momentary impact force offset from the sweet spot, atorque is produced about a fixed axis through the center of mass of theputter, the beam means producing a counter-torque when the impact forcebegins to decrease.
 18. The golf putter as in claim 11 wherein thedeflection and recovery of the beam means to cause the putter face toreturn to its original putting line is the characteristic time of thebeam means.
 19. The golf putter as in claim 11 further comprising meansto connect the beam means to the wall members to allow removal andreconnection of the beam means or alternate beam means to the wallmembers.
 20. A golf putter having a shaft and a putter head, said putterhaving a given center of mass and further comprising: a body having afront member with a putter face having a sweet spot, a rear section,perimeter wall members, and actively compliant beam means beingpositioned nearer the putter face than the rear section, the beam meansfor storing energy produced by the force of putter face impact with agolf ball, the beam means being particularly configured to deflect uponputter face impact with a golf ball, the deflection of the beam meansbeing greater than the golf ball impact deflection of the putter face,whereby when the putter face impact with the golf ball is offset fromthe sweet spot of the putter face, a torque is produced about a fixedvertical axis through the center of mass of the putter, the beam meansproducing a counter- torque when the force produced by the impact beginsto decrease, said beam means being located rearward of the front member,positioned parallel to the putter face and extending uninterruptedbetween and connected directly to the perimeter wall members, and meansfor attaching the shaft directly to the beam means at a location betweenthe perimeter wall members.
 21. The golf putter as in claim 20 whereinthe beam means comprises a central member interconnected between twolateral beam members.
 22. The golf putter as in claim 20 wherein thebeam means comprises a single beam extending between perimeter wallmembers.
 23. The golf putter as in claim 20 whereby the shaft isattached at an angle greater than 10 degrees from a vertical plane. 24.The golf putter as in claim 20 wherein the body includes two perimeterwall members.
 25. The golf putter as in claim 24 wherein the perimeterwalls comprise a rearward section and a forward section and the beammeans extends from these two sections.
 26. The golf putter as in claim20 wherein the sweet spot of putter face is to be aligned with a desiredputting line whereby the deflection of the beam means and simultaneousrecovery of the beam means, causing the putter face to return to thedesired putting line at almost the same instant the ball leaves theputter face.
 27. The golf putter as in claim 26 wherein the deflectionand recovery of the beam means to cause the putter face to return to thedesired putting line is the characteristic time of the beam means. 28.The golf putter as in claim 20 further comprising means to connect thebeam means within the body to allow removal and reconnection of the beammeans or alternate beam means within the body.
 29. A golf putter havinga shaft and a putter head with a putter face having a sweet spot, saidputter having a given moment of inertia which produces forcesperpendicular to the center of mass of the putter when there is putterhead impact with a golf ball offset from the sweet spot, said putterhead comprising: a body having a front member with said putter face, arear section, perimeter wall members, and deflection means for storingenergy produced upon putter face impact with a golf ball, the deflectionmeans being particularly configured to flex upon putter face impact witha golf ball, the flexure of the deflection means being greater than thegolf ball impact flexure of the putter face, whereby the energy storedwithin the deflection means causes a decrease in the dynamic moment ofinertia of the putter, resulting in an overall increase in the feel ofthe putter, said deflection means being positioned parallel to theputter face and nearer the putter face than the rear section, and meansfor attaching the shaft directly to the deflection means at a locationbetween the perimeter wall members.
 30. The putter as in claim 29wherein an increase in overall feel of the putter is caused by anincrease in magnitude of sense of touch of the putter.
 31. The putter asin claim 30 wherein the increase in the feel of the putter is a tactilefeel.
 32. The putter as in claim 30 wherein the increase in the feel ofthe putter is a kinesthetic feel.
 33. The putter as in claim 30 whereinthe increase in the feel of the putter is a visual feel.
 34. The putteras in claim 30 wherein the increase in the feel of the putter is anintuitive feel.
 35. The putter as in claim 30 wherein the increase inthe feel of the putter is a sound feel.
 36. The putter as in claim 35wherein a range of sound feel frequencies of the putter is between 1000to 4000 hz.
 37. The putter as in claim 36 wherein the moment of inertiaof the putter is in a range of 2000 to 8000 grams*cm².